Consecutive terms of a sequence are related by Un+1=(Un−3)2+2U_{n+1} = (U_n - 3)^2 + 2Un+1=(Un−3)2+2.
(i) In the case where U1=2U_1 = 2U1=2, find U3U_3U3. (ii) Find U20U_{20}U20.
State a different value of U1 U_1\,U1 that would give the same value for U20U_{20}U20 found in part (a)(ii).
178 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.